Evaluate | F· dr where F(x, y, z) (4yz cos(xyz), 4xz cos(xyz), 4xy cos(xyz)) and C is the line C 1 to the point ( 7, 1 segment joining the point ( 10, 2' 10 6

Q: The function f(z) =e² is: u(x.y)=e*cos(y) o u(x,y) =e*sin(y) ¤ contiuous in СО discontiuous in CO

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Q: Let f(x, y, z) = ln () Vxy – sin (cos (zy)) , evaluate ху %3D дх ду

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A: Given,        F(x, y, z)=sinyi+xcosyj-sinzk.

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Q: Evaluate | f(x,y) ds where Cis the portion of the curve y = In x from the point (1,0) to the point…

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Q: Evaluate F. dr where F(x, Y, z) = (1.25yz cos(xyz), 1.25xz cos(xyz), 1.25xy cos(xyz)) 1 1 and C is…

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Q: Evaluate F · dr where C is the line segment from (2, -, 1) to (94, 1, and 2 2 F = (sin(yz) + 1)i +…

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Q: . Verify that u(x, y) = xy+7x +e° onjugates v(x, y) and find an expression for f(2) = f(x+iy) = u(x,…

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Q: Evaluate ∫ ▽f*dr Where f(x,y,z)=cos(πx)+sin(πy)-xyz and C is any path that starts at (1,1/2,2) and…

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Q: Consider the functions z=7 ex In y, x= In (u cos v), and y= u sin v. dz dz (a) Express and as…

A: Given, z= 7 ex ln y    ....... (1)x= ln ( u cosv) .......... (2)y= u sinv…

Q: Find a potential function for F or determine that F is not conservative. F = (cos(z), 16y, -x…

A: The vector field given in the question is: F = <cos(z), 16y, -xsin(z)> Hence, F1 = cos(z), F2…

Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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Q: 2. Let F = 3.xyz i – 4xyz j + 2xyz k . Find div F and curl F. -

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Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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Q: directional derivative

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Q: Find an antideriuative Flx) of the functian f(x) = 8 sinx such that FlO)=D1 %3D 13 + COSX

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Q: Find the Wronskian of the functions f(t) = et sin(t) and g(t) = et cos(t). NOTE: Your answer must be…

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Q: (B) Find analytic function f(z) =u +iv such that, d Im dz 2x +e* cos y is analytic function.R x² +y…

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Q: Consider the function f defined by f(r,y) = exp(kr) cos(ky) for k > 0 Evaluate frr(x, y) Evaluate…

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Q: Find fæ, fy, and fz. 4.5 f (x, Y, z) = 4z In(x*y° cos(5z))

A: To find the partial derivatives with respect to x ,y ,z.

Q: Show that f(z) is differentiable and Evaluate f'(z) if f(z) = u(x, y) + iv(x,y), where %3D u(x, y) =…

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Q: Linearizations for Three VariablesFind the linearizations L(x, y, z) of the functions in Exercises…

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Q: Let r(t) = (sin(t), cos(t), 5 sin(t) + 4 cos(2t)). Find the projection of r(t) onto the xz-plane for…

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Q: Find f, fy, and f. f (r, y, z) = z In (a*y® cos(2z)) f%3= fy = %3D fz =

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Q: Show that f(z) is differentiable and Evaluate f'(z) if f(z) = u(x,y) + iv(x, y), where %3D u(x, y) =…

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Q: Find the work done by F over the curve in the direction of increasing t. F = 3xyi + 4yj - 2yzk r(t)…

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Q: Use Stokes's Theorem to evaluate F(x y₁ z) = x² +2 - xyzk F. dr. In this case, C is oriented…

A: The solution is given below

Q: 3. Find the work done by F over the curve in the direction of increasing t. = (2,x, y) = (sin t, cos…

A: Write the vector field F=zi+xj+yk The equation of the curve. rt=sinti+costj+tk Differentiate…

Q: (2) Use Green's theorem to calculate f. F - di for F(x, y) = (x2 + y, e") and C the boundary of the…

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Q: Let z = f(x, y), x = rcos 0 and y = r sin 0. Evaluate the value of zg at the point (x, y) = (/3,1)…

A: Chain rule: If is function of and and are functions of and then, Given:

Q: 1. Sketch in the xy - plane the domain of each function : (a) ƒ (x, y) = (Vx – 1+ Vy +1) · In (x² +…

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Q: 2. Let F(x,y) = (cos(x – 2y), –2 cos(x – 2y)). Find curves C and C2 so | that, F. dr = 0 F. dr = 1

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Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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Q: - Let f(z) = cosh z. (1) Find the image of S := {z = x+iye C: x < 0,0 < y < } under f.

A: Follow the steps.

Q: Find fæ, fy, and fz. f(z, y, z) = z In(a"y cos(5z) 4.3 = z In (x*y° cos(52)) fr = fy = f: =

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Q: Find fa, fy, and fz. f (x, y, z) = z In(xʻy° cos(52)) 4,3 COS x*Y fn = fy = fz =

A: Please refer the attached image for complete solution.

Q: (b) If F = (5xy- 6x )i + (2y– 4x)j, Evaluate [F.dr along the curve C in the xy-plane, y =x' from the…

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Q: Let f(x, y) = y cos (xy), then f.(x, y) = fy(x, y).

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Q: Show that U (x, y) = e"cos v,V(x, y) = e"sin v are conjugate harmonic of each other if f = u + iv is…

A: Solution given below

Q: Evaluate F. dr where F(x, y, z) = (3.75yz cos(xyz), 3.75xz cos(ryz), 3.75xy cos(xyz)) and C is 1 1…

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Q: 3. Let f(x, y) = xy² + x°y². Find an equation for the tangent plane at (x, y) (-1,2). %3D

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Q: Let C denote the curve of intersection between x = -5z° and y = 6z", starting from A(0,0,0) and…

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Q: find div and curl F F(x,y,z)= 7y3z2i- 8x2z5j-3xy4k F(x,y,z) = exyi-cosy j +sin2 z k

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Q: Let U (x, y) = e-(y sin x Find a real-valued function V (x, y) such that f(z) = U + iV is analytic.…

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Q: Consider f(t) = (cos t, sin t, t²) and g(x,y,z) = (x² + y² + z², 3x + 4y –- 12z) and h = g(f(t)) =…

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Q: 2. Show that fxy and fyx are equal for the function f(x, y) = x²y sin(x + y). %3D xy. cos(xry) + 2xy…

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Q: B) Use Green's Theorem to evaluate /F-dr, where C is a triangle from (0,0) to (1,0) to (0,3) to…

A: We will use Greens theorem here

Q: Let f(z) = sin(z'). %3D s'(z) = 3 coslx 3)) 2. 3x cos(X %3D S'(4) = 0

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